This is interesting. While again these numbers are not perfect (sample sizes of about 130 crits, ideally you'd want something like ten times that), it seems that 2.0 is close to the worst possible attack speed. After that, your proc rate actually starts to scale better with attack speed (from 2 to 3 APS is a ~20% proc rate increase, from 3 to 4 is about 25%). My assumption is that this is due to you essentially having lots of "free attempts" with a high attack speed - you still get just as many chances to proc as a lower attack speed build, just not in a row, so the numbers you get are skewed to the high side of the theoretical maximum.

So the question now is, do you bother with attack speed? It does not seem to be an easy question to answer. 3 APS gets about 20% more procs than 1.5 APS, but obviously requires a lot of effort to reach, and this could alternatively be channeled into survivability or spell damage. Thoughts?

Actually, now that I look at your process more, this makes a lot of sense.

At 2.0 APS base, a GMP-linked Barrage hits, on mean average, every 0.0625 seconds, but remember how Barrage works? A large chunk of the attack time is actually spent winding up each Barrage, which takes up at least 25% of the attack time. With that taken into consideration, each projectile of the Barrage attack will hit 0.046875 seconds apart, just inside of the 0.05 second cooldown, leading to high wastage.

With a GMP Barrage, the point of this high wastage is actually between 1.82 and 2.0 aps. If I had to guess, it's somewhere around 1.95 aps, but I'm not positive about the exact value.

Playing PoE for a long time, but I never did a CoC build, ever... can you pls explain in more detail how it's possible that both a 1.5APS and a 2.5APS are better than 2APS. Not exactly ELI5, but near that :D

CoC has an internal 50ms cooldown to proc spells. So ideally, you want to hit things with a crit every 51ms. With about 2.0 aps, you're hitting enemies after every about 48ms, which means you can never get two procs in a row.

With low aps, every crit will be a proc. With high aps, you can start hitting every 26ms (ideal) which means you'll hit right after the cooldown every time (52ms), but if you don't crit you'll get another chance in only 26ms.

The ideal "break points" are 51ms, 26ms, 17ms, 13ms, etc. All numbers that have an integer multiple just above 50ms.

That explanation assumes that Mark was wrong here, which is not out of the question but seems odd. It also can't explain table 2 if I understand you correctly, since it still depends on the idea of a clean threshold, which is inconsistent with the behaviour displayed.

i don't know how it worked way back in august '14 when that post was made but currently after doing some very quick and extremely rough timing, the attack time listed in the tooltip is accurate to the time it takes to complete the whole barrage including the windup/down as well as with or without GMP (the windup by itself takes up what seems to be half the total time? the wind down a good bit less? needs better testing) so adding projectiles does not seem to add more time to the barrage but rather reduces the time spent firing each projectile.

and each projectile takes a set percentage of the attack time for itself.

if this is the case, then that % changes depending on the number of projectiles. ie, more projectiles = less % time taken for each. if he meant that a % of the total attack time is given to firing projectiles, then that would be correct since the total time spent is accurate to the tooltip attack time.

i have no idea about the rest but i imagine that you would want to keep the time between each projectile over .025 to avoid overlapping a third projectile on CoC's cooldown timer, which i think is where the wastage is coming from as you approach 2 aps.

Huh, well I see where I got 40% from, now, but if that's how it works then that means each attack would be using less than 10% of the attack time, meaning that in addition to the 40% windup there's also a 20%ish wind-down. It's also possible that Mark was slightly wrong, and the remembered figure of 40% is less than the actual windup time.

There was a Reddit post some time ago that did some testing on how Barrage handles the attack time that had some more precise figures. I don't remember the title or anything else about it, though, so Google isn't working for me.

When I consulted GGG about this last time, I was told that adding GMP to Barrage means that the stated attack time becomes incorrect: It's still the time of windup + shoot 4 projectiles, but the time you're actually taking is windup + shoot 8 projectiles.

Can you verify (maybe with video footage) that GMP Barrage attacks with 2.0 aps will actually result in 2 attacks per second?

No, I can't. It isn't possible. I tried to look at the relationship between Barrage and extra projectiles based on the information you're citing a while ago (see here), and it was a complete mess, behaving totally inconsistently. Going off this post, there basically is no way to test it properly. I have repeated this using lockstep post-2.0 and it is exactly the same.

However, this current investigation doesn't really care about this relationship, which is partially why I chose the methodology I did. I'm only interested in the final proc rate, which is the only thing people actually need to be interested in to plan their builds. That said, I might well take a look at doing some of the same testing without GMP, just to see what the differences are.

Wouldn't that still result in the procs per crit being constant and then dropping at a threshold and just change where the threshold is?

If the OP's data is correct, the procs per crit steadily drops as your attack speed increases, rather than there being strict thresholds. This means that the projectiles must not be evenly distributed (whether over the entire attack time or just part of it). It's possble they're distributed somewhat randomly, or that for some reason it's deterministic but uneven.

Yeah, it's a definite possible explanation for why the popular calculation of 2.0-2.2 APS could be wrong and 1.8-2.0 might be more accurate, but the steady decrease instead of the sudden threshold is still very important and mysterious. Overall, if this data is all correct it looks like attack speed is being seriously overrated for Barrage CoC builds. Right now I think having an attack speed just below the threshold is considered very strong, but this makes it look like attack speed isn't very significant at all unless you can get a huge amount of it.

I think the key is to avoid anything between 1.85 and 2.1 APS or so. Attack Speed is less effective than expected for some unknown reason, but I think getting enough attack speed to get past the threshold is going to result in more consistent DPS since shorter overall attack times means your non-crit attacks take less time, and I also think that it's not always practical to just avoid Attack Speed as much as possible since it's still not a bad stat and most builds will likely wind up with some incidental attack speed regardless.

So I tried writing a Python script to simulate how many procs you'd get per crit if the projectiles occurred at a completely random time during the attack time, instead of evenly spaced. This was based on the idea that the gradual decrease in procs per crit (as opposed to it being suddenly halved after a threshold as many people predicted) could be explained by the projectile times not being consistent.

Here's the results. I cannot promise that my methodology is correct and my code is bug free:

Speed: 1.1, Procs: 4.375

Speed: 1.2, Procs: 4.289

Speed: 1.3, Procs: 4.152

Speed: 1.4, Procs: 4.125

Speed: 1.5, Procs: 4.047

Speed: 1.6, Procs: 3.927

Speed: 1.7, Procs: 3.876

Speed: 1.8, Procs: 3.837

Speed: 1.9, Procs: 3.806

Speed: 2.0, Procs: 3.699

Speed: 2.1, Procs: 3.656

Speed: 2.2, Procs: 3.631

Speed: 2.3, Procs: 3.57

Speed: 2.4, Procs: 3.498

Speed: 2.5, Procs: 3.413

Speed: 2.6, Procs: 3.445

Speed: 2.7, Procs: 3.359

Speed: 2.8, Procs: 3.306

Speed: 2.9, Procs: 3.243

Speed: 3.0, Procs: 3.238

Speed: 3.1, Procs: 3.181

Speed: 3.2, Procs: 3.084

Speed: 3.3, Procs: 3.134

Speed: 3.4, Procs: 3.057

Speed: 3.5, Procs: 2.978

Speed: 3.6, Procs: 2.989

Speed: 3.7, Procs: 2.95

Speed: 3.8, Procs: 2.92

Speed: 3.9, Procs: 2.862

Speed: 4.0, Procs: 2.852

Speed: 4.1, Procs: 2.797

Speed: 4.2, Procs: 2.808

Speed: 4.3, Procs: 2.722

Speed: 4.4, Procs: 2.705

Speed: 4.5, Procs: 2.691

Speed: 4.6, Procs: 2.652

Speed: 4.7, Procs: 2.653

Speed: 4.8, Procs: 2.616

Speed: 4.9, Procs: 2.57

Speed: 5.0, Procs: 2.57

So, assuming my code's working correctly, it looks like the projectiles don't occur randomly during the attack window. While that would result in procs per crit decreasing gradually as attack speed increases instead of sharply, the numbers don't seem to line up: that would give move procs per crit at very high attack speeds, but less at low ones.

Yeah, the fact that I hit the theoretical mean proc rate on my slowest test (level 17 CoC = 5.28 procs per 8 hits on average, which is exactly what I observed with 1.1 APS) also seems to count against it being totally random. It might still have a small degree of random spread though.

Is there a way to test whether this could be due to rounding? I'm guessing not without having a better idea of Barrage's screwy mechanics...

Yeah, beyond guessing things, doing tests/calculations, and seeing if they match your results, I'm not sure how much we can figure out here beside the conclusion you've already come to: Attack speed is less threshold-based on CoC barrage builds than believed, and also probably considerably less valuable than previously believed (considering the investment required to get enough speed to make a significant difference can almost certainly give a bigger damage boost if spent elsewhere, considering the sheer amount of speed needed).

Have you considered testing it without GMP to see if that changes things? I wonder if attack speed being overrated means GMP's overrated as well.

I have, but I considered it to be fairly low-priority since people would likely use it for the spread anyway. That said, I suppose there's potential for a non-projectile-spell Barrage build that doesn't bother with GMP. Might take a look at it tomorrow.

I did a very similar thing for the current assumption of linear spacing (not random).., but manually. Each permutation was written out and then the chance for that permutation occurring was weighted based on level 20 CoC.

I do agree though that the projectiles must not be distributed linearly in a single Barrage attack. They might be exponentially distributed (i.e. not every projectile will be exactly 0.05 seconds apart, the value may be decreasing as you fire more projectiles) This would explain why Im never able to proc 8 SRS while under "breakpoint," even though i should have 5.7% chance of doing so.

That's different from a manual calculation of what I did, since what I was testing didn't have a finite number of permutations. The conclusion is similar, though. The distribution of projectiles over the attack time seems to be neither completely random nor completely even.

You're right, I just realized it and edited the post. Good to have two contrasting data sets, though. Now all we have to do is test to see if those aps result in similar numbers to your model... Rounding is a huge issue though, because when one spell is triggered you must have a way of enforcing a "cooldown" period where no other spells can be procced.

The only possible conclusion here is the one that OP suggested in the forum post: The shots are not completely evenly distributed. Really nice research btw!! can certainly be improved but that requires a lot of work. Love your PvP, SRS method

Could anybody give a TL;DR of sorts? I've hardly touched CoC/Barrage so I can't really comment on how it all works exactly. If you're using Barrage for CoC is it best to mostly focus on crit/accuracy while getting little attack speed?

If you got a low crit chance. Attack speed is good since you get more chance to proc it. And should be the same with high crit chance since. You get more chance to trigger it. But i think there is a point when ur 95% chance to crit and there is a 50ms cooldown on crit. Do there would be some downtime on your coc.